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16.11.2020 •

Mathematics

Carlos pays $25 for skis and borrows the remaining amount. The loan payments are $75 every 3 months for one and a half years. The interest rate is 16.2%/a compounded quarterly. What was the selling price of the skis? a) $392.52

b) $417.52

c) $367.52

d) $523.10

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Ответ:

Nekomancer5291

21.01.2023

Mathematics

Step-by-step explanation:

Given,

In triangle ABC,

AC = 12 unit,

m∠A = 30°,

m∠B = 45°,

Let D∈AB such that CD ⊥ AB,

In triangle ADC,

$sin A = \frac{CD}{AC}$

$sin 30^{\circ}=\frac{CD}{12}$

$\frac{1}{2}=\frac{CD}{12}$

$\implies CD=6\text{ unit}$ ,

By the pythagorean theorem,

$AC^2=CD^2+AD^2\implies 144 = 36 + AD^2\implies 108=AD^2\implies AD=6\sqrt{3}\text{ unit}$

Now, in triangle CDB,

$tan 45^{\circ}=\frac{CD}{DB}$

$1=\frac{6}{DB}\implies DB=6\text{ unit}$

$AB=AD+DB=6\sqrt{3}+6=6(\sqrt{3}+1)\text{ unit}$

Hence, the area of the triangle ABC = $\frac{1}{2}\times AB\times CD$

$=\frac{1}{2}\times 6(\sqrt{3}+1)\times 6$

$=18(\sqrt{3}+1)\text{ square unit}$

Option 'C' is correct.

In triangle abc, ac =12, the measure of angle a = 30, and the measure of angle b = 45. find the area

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Carlos pays $25 for skis and borrows the remaining amount. The loan payments are $75 every 3 months for one and a half years. The interest rate is 16.2%/a compounded quarterly. What was the selling price of the skis? a) $392.52b) $417.52c) $367.52d) $523.10